At the age of 16, in 1940, Dynkin was admitted to Moscow University. He avoided military service in World War II because of his poor eyesight, and received his M.S. in 1945 and his Ph.D. in 1948. He became an assistant professor at Moscow, but was not awarded a "chair" until 1954 because of his political undesirability. His academic progress was made difficult due to his father's fate, as well as Dynkin's Jewish origin; the special efforts of Andrey Kolmogorov, his Ph.D. supervisor, made it possible for Dynkin to progress through graduate school into a teaching position.[3]

Dynkin is considered to be a rare example of a mathematician who made fundamental contributions to two very distinct areas of mathematics: algebra and probability theory.[8] The algebraic period of Dynkin's mathematical work was between 1944 and 1954, though even during this time a probabilistic theme was noticeable.[9] Indeed, Dynkin's first publication was in 1945, jointly with N. A. Dmitriev, solved a problem on the eigenvalues of stochastic matrices. This problem was raised at Kolmogorov's seminar on Markov chains, while both Dynkin and Dmitriev were undergraduates.[9]

While Dynkin was a student at Moscow University, he attended Israel Gelfand's seminar on Lie groups. In 1944, Gelfand asked him to prepare a survey on the structure and classification of semisimple Lie groups, based on the papers by Hermann Weyl and Bartel Leendert van der Waerden. Dynkin found the papers difficult to read, and in an attempt to better understand the results, he invented the notion of a "simple root" in a root system. He represented the pairwise angles between these simple roots in the form of a Dynkin diagram. In this way he obtained a cleaner exposition of the classification of complex semisimple Lie algebras.[10] Of Dynkin's 1947 paper "Structure of semisimple Lie algebras", Bertram Kostant wrote:

In this paper, using only elementary mathematics, and starting with almost nothing, Dynkin, brilliantly and elegantly developed the structure and machinery of semisimple Lie algebras. What he accomplished in this paper was to take a hitherto esoteric subject, and to make it into beautiful and powerful mathematics.

Dynkin is considered one of the founders of the modern theory of Markov processes. The results obtained by Dynkin and other participants of his seminar at Moscow University were summarized in two books. The first of these, "Theory of Markov Processes", was published in 1959, and laid the foundations of the theory.